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Q. No.A spring of stiffness \(k\) is compressed a distance \(x,\) and a toy car is placed against it. If the car has a mass \(m,\) which equation represents the final speed of the car after the spring is released to accelerate the car?
| 1. | \(v=\sqrt{\frac{kx^2}{m}}\) | 2. | \(v=\sqrt{\frac{m}{kx^2}}\) |
| 3. | \(v=\sqrt{\frac{mx^2}{k}}\) | 4. | \(v=\sqrt{\frac{k}{mx^2}}\) |
Subtopic: Â Elastic Potential Energy |
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Level 1: 80%+
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Two springs of spring constants \(k_1\) and \(k_2\) are attached in series. The work done in stretching the spring by a small length \(d\) is:
1. \(\dfrac{1}{2}\left(\sqrt{{k}_{1}{k}_{2}}\right){d}^{2}\)
2. \(\dfrac{1}{2}\left({{k}_{1}{+}{k}_{2}}\right){d}^{2}\)
3. \(\dfrac{1}{2}\left(\dfrac{{k}_{1}{k}_{2}}{{k}_{1}{+}{k}_{2}}\right){d}^{2} \)
4. \(\dfrac{1}{3}\left(\dfrac{{k}_{1}{k}_{2}}{{k}_{1}{+}{k}_{2}}\right){d}^{2}\)
1. \(\dfrac{1}{2}\left(\sqrt{{k}_{1}{k}_{2}}\right){d}^{2}\)
2. \(\dfrac{1}{2}\left({{k}_{1}{+}{k}_{2}}\right){d}^{2}\)
3. \(\dfrac{1}{2}\left(\dfrac{{k}_{1}{k}_{2}}{{k}_{1}{+}{k}_{2}}\right){d}^{2} \)
4. \(\dfrac{1}{3}\left(\dfrac{{k}_{1}{k}_{2}}{{k}_{1}{+}{k}_{2}}\right){d}^{2}\)
Subtopic: Â Elastic Potential Energy |
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Level 1: 80%+
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A block of mass \(m\) is moving with initial velocity \(u\) towards a stationary spring of stiffness constant \(k\) attached to the wall as shown in the figure. Maximum compression of the spring is:
(The friction between the block and the surface is negligible).
| 1. | \(u\sqrt{\dfrac{m}{k}} \) | 2. | \(4u\sqrt{\dfrac{m}{k}}\) |
| 3. | \(2u\sqrt{\dfrac{m}{k}}\) | 4. | \(\dfrac12u\sqrt{\dfrac{k}{m}}\) |
Subtopic: Â Elastic Potential Energy |
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Level 1: 80%+
NEET - 2022
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A block of mass \(m\) is attached to an unstretched spring with a spring constant \(k\) placed on a smooth horizontal table. The block is now pulled to a displacement of \(x_{m}\) and then released. The maximum speed it will attain will be:
| 1. | \(\sqrt{\dfrac{k}{m}}x_m\) | 2. | \(\sqrt{\dfrac{m}{k}}x_m\) |
| 3. | \({\dfrac{k}{m}}x_m\) | 4. | \({\dfrac{m}{k}}x_m\) |
Subtopic: Â Elastic Potential Energy |
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Level 1: 80%+
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A ball of mass \(m\) is projected with a speed \(u,\) at an angle of \(\theta\) with the horizontal. At its highest point, it moves on a smooth horizontal platform with a spring of spring constant \(k\) attached, and the ball compresses the spring. The maximum compression in the spring is \(x.\) Then:
1. \(\dfrac12mu^2=\dfrac12kx^2\)
2. \(\dfrac12mu^2cos^2\theta=\dfrac12kx^2\)
3. \(\dfrac12mu^2=\dfrac12kx^2cos^2\theta\)
4. \(\dfrac12mu^2sin^2\theta=\dfrac12kx^2\)
1. \(\dfrac12mu^2=\dfrac12kx^2\)
2. \(\dfrac12mu^2cos^2\theta=\dfrac12kx^2\)
3. \(\dfrac12mu^2=\dfrac12kx^2cos^2\theta\)
4. \(\dfrac12mu^2sin^2\theta=\dfrac12kx^2\)
Subtopic: Â Elastic Potential Energy |
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Level 2: 60%+
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Q. No.
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